What is X in the sequence 24, X, 12, 18, 36, 90?

1. A. 18
2. B. 12
3. C. 9
4. D. 6

Answer: B

Explanation

Let’s analyze the pattern in the given sequence: 24, X, 12, 18, 36, 90.
Observe the relationship between the known consecutive terms:
– 12 to 18: 12 × 1.5 = 18
– 18 to 36: 18 × 2 = 36
– 36 to 90: 36 × 2.5 = 90

The multipliers are increasing by 0.5 each time (1.5, 2, 2.5). Following this pattern backward, the multiplier for the term before 12 should be 1, and the multiplier for the term before that (24) should be 0.5.
So, 24 × 0.5 = 12.
And, 12 × 1 = 12.
Therefore, X = 12. The complete sequence with the pattern is 24, 12, 12, 18, 36, 90. This question tests pattern recognition and logical deduction skills, which are fundamental to the Logical Reasoning section of UPSC CSAT.